Rocker shoes for prescribed ankle motion

ABSTRACT

A method is provided for providing a shoe sole profile shape for an individual who has a prescribed ankle angular motion for at least a partial heel-to-toe foot motion of the individual. A shoe sole geometry is determined that provides a substantially invariant roll-over shape for level ground walking that accommodates the prescribed ankle angular motion of the individual. The shoe sole geometry then is imparted to a shoe sole by machining, molding or other shaping operation.

This application claims benefits and priority of U.S. provisional application No. 61/211,976 filed Apr. 6, 2009, the disclosure of which is incorporated herein by reference.

CONTRACTUAL ORIGIN OF THE INVENTION

The invention was made with government support under Grant No. 1 R03 HD050428-01A2 awarded by the National Institute of Health. The Government has rights in the invention.

BACKGROUND OF THE INVENTION

Rockers have been used by many investigators to describe walking. Perry (1992) described the functions of the foot and ankle as creating three rockers to facilitate forward progression during walking: the heel rocker, ankle rocker, and forefoot rocker. Morawski and Wojcieszak (1978) studied the use of rockers in walking toys and suggested that rockers could be useful for the design of prostheses and orthoses. McGeer (1990) created mathematical and physical models of mechanisms that could walk down gentle slopes using only passive dynamic properties (i.e. without the use of external power). A key component of McGeer's model was the circular rocker used to replace the function of the foot and ankle. McGeer (1990) suggested that the “equivalent radius” for human walking would be roughly 0.3 times the length of the leg based on a simple model and calculation. Collins et al. (2005) have developed even more lifelike walking machines that incorporate rockers in place of the feet and ankles, and that are able to walk on level ground. Wisse and van Frankenhuyzen (2003) demonstrated that increasing the radius of the rocker on a passive dynamic walking machine increases the amount of disturbance it can tolerate without falling down. Adamczyk et al. (2006) examined the effects of wearing rocker boots on metabolic rate of able-bodied ambulators. Subjects were asked to walk at 1.3 meters/second on a treadmill while wearing rigid-ankle walking boots connected to wooden rockers. The metabolic rate was estimated from respiratory gas exchange data measured during the treadmill walking trials and was examined as a function of rocker radius. Adamczyk et al. (2006) found that the subjects walked with a minimum metabolic rate when the rocker radius was approximately 0.3 times the leg length, matching the “equivalent radius” suggested by McGeer (1990). These studies suggest that rockers are important for robust and efficient bipedal ambulation.

Perry et al. (1981) studied the effectiveness of a simple rocker bottom shoe for restoring walking function for several women with multiple sclerosis. The rocker shoes were found to be beneficial to three women in the study with “obstructive spasticity”, helping them improve their self-selected walking speed from 55% to 103% of normal speeds used by able-bodied persons. Energy cost in this subject group was reduced from 717% to 93% of the cost used by able-bodied persons when switching from normal shoes to rocker shoes. The rocker shoe used in Perry et al.'s (1981) study had a “roll point” (transition point from a flat to a rolling surface) located at 60% of the sole length referenced from the posterior edge of the shoe sole. The authors stated, “When this distance was shorter, shoes rolled too fast and when longer, shoes offered no walking assistance.” Other subjects in the study derived benefit from the rocker shoes, though on a smaller scale.

Peterson et al. (1985) compared the gait characteristics of able-bodied persons walking with rocker shoes and unaltered athletic shoes. Most gait parameters were found to be similar between shoe conditions, but it was noted that the ankle movements of the participants were offset into plantarfexion with the rocker shoe to accommodate the 8.5-degree heel height difference between the rocker shoe and the athletic shoe. Other studies have suggested that able-bodied persons offset their ankles into more plantarflexed positions to accommodate high-heeled shoes (Opila et al., 1988; de Lateur et al., 1991).

Many investigators have measured plantar pressures between the feet and shoes of persons when wearing regular shoes and various styles of rocker shoes (Praet and Louwerens, 2003; Schaff and Cavanagh, 1990; Postema et al., 1998; Nawoczenski et al., 1988; Mueller et al., 1997; Brown et al., 2004; van Schie et al., 2000). Most of the studies found that rocker shoes help to reduce the peak pressures under the metatarsal heads at the expense of higher peak pressures in the midfoot. This finding is relevant to the diabetic population, particularly persons with peripheral neuropathy, who have problems with skin breakdown and can develop ulcers under the metatarsal head regions of their feet. However, it was noted in several of the studies that the response is variable between persons and it was suggested that plantar pressure measurement be used clinically to determine proper rocker characteristics for each individual. A better understanding or theory to describe the effects of shoe rockers on the physiologic system could be beneficial because it could suggest predictive factors for the success of rocker shoes for various patient populations. If predictive factors are found to be valuable, their use could be implemented into clinical practice.

Rocker shoes have been described in the literature as being useful for several purposes, including the treatment of persons with metatarsophalangeal joint synovitis (Trepman and Yeo, 1995), calf claudication (Richardson, 1991), sesamoid disorders (Rosenfield and Trepman, 2000) , plantar ulcers resulting from diabetes (Mueller and Diamond, 1988), and transmetatarsai amputations resulting from diabetes (Mueller and Strube, 1997). Rockers are commonly used on walking casts and walking boots. Hullin and Robb (1991) studied eleven commercially available rockers for application to lower limb casts and found that only two gave walking characteristics that approached that of able-bodied walking. Both of these two attachable rockers were cams, but specific data regarding their radii were not presented. A study by Crenshaw et al. (2004) examined the effect of the locked position of the ankle in a walking rocker boot on plantar pressures between the plantar surface of the foot and the walking boot. Contrary to clinical expectations, it was found that dorsiflexed positions of the ankle caused increased pressures on the forefoot and reduced pressures on the heels of able-bodied subjects in the study. Also, plantarflexed positions of the ankle were found to cause increased plantar pressures on the heel and reduced pressures on the forefoot regions of the subjects' feet. These results suggest that, in spite of the constraint on ankle motion, the able-bodied subjects may have been attempting to compensate for the misalignments within the boot causing the measured changes in plantar pressures.

Milgram and Jacobson (1978) described many possible alterations for shoes to treat disability of the feet and ankles. A shoe with a continuous radius rocker from heel to toe was said to provide an “ankle on the ground”, suggesting that the effect of the ankle could be placed into the rocker, eliminating the need for true ankle rotation.

Knox (1996) examined static and dynamic mechanical properties of many prosthetic feet and stated that effective foot shape is key to their function for walking. Knox's work showed that the effective rocker shape of a prosthetic foot, which gradually develops as the foot deforms under the loading conditions of walking, affects the gait of its user. Knox (1996) developed a simple method for measuring the effective rocker shape of the ankle-foot system, and used the method to measure the rocker shapes (referred to later as “roll-over shapes”) of both able-bodied and prosthetic ankle-foot systems. The Shape Foot, a block of wood cut into a rocker shape and made to attach to a lower limb prosthesis, was developed by our laboratory in the 1990s (Knox, 1996). The Shape Foot proved that simple feet could be produced that would have good walking function if an effective rocker shape were used as a main design constraint.

Further work in applicants' laboratory led to the development of the Shape&Roll prosthetic foot, a foot made of plastic material (e.g. a copolymer polypropylene/polyethylene) that is inexpensive and that takes a biomimetic shape when loaded during walking (Sam et al., 2004). During development of the Shape&Roll prosthetic foot, questions arose concerning the specific effective rocker shapes that should be used in the design, particularly as amputees encounter the different walking conditions of daily life. It was decided to examine the effective rockers used by able-bodied persons during walking and to consider these rockers as the gold standard for development of the Shape&Roll prosthetic foot.

Examinations in applicants' laboratory of able-bodied persons walking under a variety of conditions suggest that persons maintain similar effective rocker shapes during walking. The effective rocker shape created by the foot and ankle together, the “ankle-foot rollover shape”, appears to maintain the same general form when persons walk at different speeds (Hansen et al., 2004a) and as persons walk with different amounts of weight added to their torso (Hansen, 2002; Hansen and Childress, 2005). The ankle-foot rollover shape also changes in meaningful ways when women walk with shoes of different heel heights (Hansen and Childress, 2004). When wearing shoes with high heel heights, women adapt to more plantarflexed ankle positions, causing roll-over shapes to be shifted downward. These ankle offsets appeared to cause the orientations of the rollover shapes to be similar to those when the women walked with lower heeled shoes.

Recent studies of prosthesis alignment also support the theory of invariant roll-over shape for level ground walking. Alignment of prostheses is the determination by a prosthetist of the proper position and orientation of a prosthetic foot with respect to their residual limb socket, and is found by trial-and-error using adjustable hardware in the prosthesis. Recent study of alignment indicated that experienced prosthetists adjust the alignments of various types of prosthetic feet, each having a different roll-over shape, toward a single rocker shape with respect to the residual limb socket (Hansen et al., 2003). This finding suggests an “ideal” roll-over shape that prosthetists inadvertently aim to mimic in a person's prosthesis. It seems that this “ideal” shape minimizes gait deviations and patient discomfort, and that is what the prosthetist attempts to find in the alignment process.

SUMMARY OF THE INVENTION

The present invention involves a method of customizing a profile geometry of a shoe sole to an indvidual by determining a shoe sole profile geometry that provides a roll-over shape for level ground walking that accommodates a prescribed ankle angular motion for the individual. The shoe sole profile geometry is then imparted to a shoe sole by machining, molding or other shaping operation to provide a customized shoe sole.

The present invention is advantageous in providing a method of customizing the shoe sole geometry to naturally obtain a desired ankle movement for orthopedic and other patients. A physician can prescribe a desired ankle motion for their patient (e.g. limited dorsiflexion) suffering from ankle problems/disabilities, based on their clinical expertise, and send this information to a shoe manufacturer. The shoe manufacturer can employ the present invention to determine the rocker shoe (shoe sole side profile geometry) that would result in the desired ankle kinematics prescribed by the physican, customize the sole of a standardized shoe (using a simple milling process, for example), and supply the shoes to the patient. As a result, practice of the invention allows the individual's ankle to adhere to the physican's presribed motion while also allowing the patient to walk in a manner conforming to the roll-over shape of an aveage healthy individual. Alternatively, sets of non-custom shoes can be created to match certain ankle kinematic patterns that may be desired for patients, e.g. shoes that result in no ankle movement during single limb stance may be useful for persons with ankle and foot pain.

These and other advantages of the present invention will become more apparent from the following detailed description taken with the following drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows knee-ankle-foot roll-over (rocker) shapes during walking. The circular marker indicates the ankle marker, which is the origin of the leg-based coordinate system. The foot outline is drawn for reference purposes and is not necessarily to scale.

FIG. 2A illustrates kinematics of the ankle (ankle flexion angle in degrees versus percent of the gait cycle where initial contact, contraleral toe off, contraleral initial contact, and toe off of the gait cycle are represented by vertical lines) for rocker shoes having different radius dimensions defining the shoe sole surface. FIG. 2B illustrates the respective ankle-foot roll-over shapes determined for the different-radii rocker shoes where x_(shank)/HEIGHT and y_(shank)/HEIGHT are height-normalized horizontal and vertical dimensions of the shank-based coordinate system, respectively, per Hansen et al. 2004a, which is incorporated by reference herein to this end.

FIG. 3 is a schematic view of the general approach for determining the appropriate shoe roll-over shape for prescribed ankle motion. “Spokes” are extended from the center of the arc to the invariant roll-over shape arc. At discrete points in time, the ankle is rotated and the segment of the “spoke” between the bottom of the shoe and the invariant roll-over shape arc is recorded.

FIGS. 4A-4D are schematic views illustrating a method embodiment of the invention. In this example, the ankle dorsiflexes less than normal during the single limb stance portion of the gait cycle (see respective insets of the “Prescribed” ankle motion in FIGS. 4A-4D).

FIGS. 5A and 5B are schematic views of “spokes” that can be reconstructed in the shoe coordinate frame to draw the sole roll-over shape and then translated proximally to minimize the shoe's sole height or to some desired shoe sole height.

FIG. 6A is a schematic view of the shoe with a visible roll-over sole profile formed thereon and FIG. 6B is a schematic view of the shoe finished into a more cosmetically appealing flat shoe sole wherein the void left after forming (e.g. cutting) of the roll-over profile shape in the shoe sole is filled by joining a highly compressible foam filler material to the roll-over profile shape to disguise its appearance.

DETAILED DESCRIPTION OF THE INVENTION

The present invention embodies so-called roll-over shape invariance for level ground walking wherein the roll-over shape is a measure of the effective rocker (i.e., cam) shape that the ankle-foot complex creates during walking, see FIG. 1. Roll-over shape invariance means that the roll-over shape keeps a consistent geometry for many conditions of level ground walking including walking at different speeds and while carrying different amounts of added weight.

In particular, the present invention embodies observations of a 25 year old able-bodied female and others who participated in a pilot study to indicate the effective rockers used during walking, standing, and swaying. A modified Helen Hayes marker set (Kadaba et al., 1990) was placed on the subject. For each of the tasks, the subject's center of pressure of the ground reaction force was transformed from a laboratory-based coordinate system to a leg-based coordinate system. The leg-based coordinate system was created in the sagittal plane using the ankle marker as the origin. The y-axis of the leg-based coordinate system went from the ankle and through a virtual hip marker (sagittal projections of these markers). The x-axis went through the ankle, was perpendicular to the y-axis, and also remained in the sagittal plane.. This method has been used by applicants to indicate the effective rocker, or rollover shape, that the physiologic knee-ankle-foot system conforms to during walking (Hansen et al., 2004a; Hansen et al., 2004b; Hansen and Childress, 2004; Hansen and Childress, 2005).

The female subject was asked to walk at her freely-selected walking speed while kinematic and kinetic data were collected. After the walking trials, the subject was asked to stand quietly for at least 10 seconds while data were collected. The subject was also asked to do small amplitude swaying in the anterior-posterior direction as well as large amplitude swaying (that required her to go up on her toes and heels) for at least 10 seconds per trial. The effective rocker that was calculated for walking is shown in FIG. 1. The circle indicates the ankle marker, the origin of the leg-based coordinate system with the ankle as the origin. A foot outline is drawn for reference and is not necessarily to scale.

The effective rocker shape ES that was calculated is shown in FIG. 1 for walking where the rocker or roll-over shape for walking is curved, substantially radius-defined arc shape and looks similar to knee-ankle-foot roll-over shapes previously reported for able-bodied ambulators (Hansen et al., 2004a).

Effective ankle-foot rocker (roll-over) shapes used by eleven able-bodied persons during walking were measured and indicated that the radius of curvature (measured as the inverse of the average curvature shape) was found to be about ⅓ of the leg length for walking.

Moreover, observations of able-bodied persons walking with various shoe sole rocker radii (different foot-shoe roll-over radii) strongly suggests that persons will drastically change their ankle kinematics, FIG. 2A, to achieve substantially the same invariant roll-over shape, FIG. 2B. FIGS. 2A and 2B resulted from experiments where shoes (high top canvas shoes; e.g. Chuck Taylor Converse All-Stars) were altered such that four rocker shoe shapes could be tested; namely, (1) flat sole (infinite radius rocker arc), (2) radius of rocker arc equal to 55% of leg length (LL), (3) radius of rocker arc equal to 40% of leg length (LL), and (4) radius of rocker arc equal to 25% of leg length (LL).

FIGS. 2A and 2B reveal that the ankle kinematic curves are changed dramtically to maintain a substantially invariant roll-over shape.

The present invention involves a method for customizing the sagittal plane shoe sole profile geometry in a manner to achieve effective rolling action (roll-over shape) of the ankle-foot-shoe system for a prescribed ankle motion of an individual walking on level ground. An illustrative embodiment of the invention involves determining a shoe sole profile geometry that provides the desired roll-over shape for level ground walking that accommodates a physican-prescribed ankle angular motion of the individual. As a result, practice of the invention allows the individual's ankle to adhere to a physican's presribed motion while also allowing the patient to walk in a manner conforming to the roll-over shape of an aveage healthy individual. The shoe sole profile geometry is imparted to a shoe sole by machining, molding or other shaping operation.

The present invention is advantageous in providing a method of customizing the shoe sole geometry to naturally obtain a desired ankle movement for orthopedic and other patients. The method of the invention gives a physician a high level of flexibility in the non-invasive treatment of their patients with ankle problems (e.g. pain). A physician treating persons with ankle problems can prescribe a desired ankle motion for their patient, based on their clinical expertise, and send this information to a shoe manufactuer. To this end, a simple-to-use software interface for determing prescribed ankle motion can be provided to physicians treating persons with ankle problems. The shoe manufacturer can employ the method of the present invention to determine the rocker shoe (shoe sole profile geometry) that would result in the prescribed ankle kinematics, customize the sole of a standardized shoe (using a simple milling process, for example), and supply the shoes to the patient. Alternatively, sets of non-custom shoes can be created to match certain ankle kinematic patterns that may be desired for patients, e.g. shoes that result in no ankle movement during single limb stance may be useful for persons with ankle and foot pain.

The physican determines a prescribed ankle motion for an individual patient based on the desire to avoid a particular range of motion or to reduce overall range of motion. A software interface package can embody a graphical user interface and be provided to the physican to allow the physican to determine the prescribed ankle motion (rotation) for an individual (patient).

An embodiment of the method of the invention involves determining a shoe sole profile geometry that provides a roll-over shape for level ground walking that accommodates the prescribed ankle angular motion of the individual as illustrated schematically in FIGS. 3, 4, and 5.

Certain patients may have pain in the ankle when it is fully loaded past a particular range of motion. One approach would be to limit the motion in an ankle-foot-orthosis (AFO), but that approach may actually lead to muscle atrophy over time. Our approach uses the person's natural tendency to maintain a consistent roll-over shape and the appropriate rocker shoe to keep the person from that range of motion using their muscles as the control actuators. This approach is much less likely to result in muscle atrophy. An example is the case where the doctor would like no movement of the ankle during single limb support, the time when the ankle is most highly loaded. In that case, our approach would produce the rocker matching the able-bodied ankle-foot roll-over shape and the muscles would hold the ankle in a constant position during that time of the gait cycle.

A virtual shoe 10 without a sole is rotated as prescribed by the physician during at least partial heel-to-toe motion of the individual. Radial “spokes” 20 are extended from the center C of the best-fit circle of the “Invariant roll-over shape” arc shown (radius=0.35 leg length where leg length is measured from greater trochanter to the floor) to the “Invariant roll-over shape” arc itself. An assumption is made that forward rolling along the shape is linearly coupled with the timeframe of the prescribed ankle motion, although other models of their association are also possible. For each point in time along the prescribed ankle motion, the ankle is rotated to its appropriate prescribed angle (see ankle rotations 1, 2, 3, 4 in the insets of FIGS. 3 and 4A-4D) and the segment 20 s of the radial spoke 20 remaining between the bottom reference surface 10 a of the shoe 10 and the “Invariant roll-over shape” arc is saved in computer memory, manually, or otherwise. That is, a radial segment (radial distance) 20 a of each “spoke” between the bottom reference surface 10 a and the “Invariant roll-over shape” arc is determined and recorded.

The radial segment 20 a is the respective radial distance between the reference shoe sole surface 10 a when the foot and shoe are rotated about the ankle to respective prescribed angles (e.g. circled 1, 2, 3, 4 in the inset of FIGS. 3 and 4A-4D) during at least partial heel-to-toe motion and the “Invariant roll-over shape arc”.

If a computer is programmed to practice the method of the invention, the computer goes through a range of incremental angles and records and stores the “spoke” segments or portions 20 s. The computer software routines embodying the invention can be used to directly determine the shoe rocker needed to obtain a particular ankle movement. The software routines can be written in MATLAB but the routines can be written in many other software languages.

No measured data goes in the computer since what the able-bodied radius tends to be relative to leg length [e.g. 0.3×leg length] is known. The computer software routines set that up and sweep through the range of contact (in angles) in heel to toe motion of the patient. Appropriate angles are chosen to sweep from the heel end of the shoe to the toe end of the shoe.

The segments 20 a of the “spokes” can be reconstructed in the shoe coordinate frame to draw the sole shape as shown in FIG. 5A. In particular, the recorded “spoke” segements or portions are reconstructed in the shoe's coordinate frame. The ends of the “spoke” segments or portions are connected by a line and extrapolated to the entire length of the shoe to create the rocker profile, FIG. 5A. Although only 4 “spokes” are shown in FIGS. 4 and 5, the computer software could create thousands or more “spokes”, leading to a smooth rocker shape when the ends are connected. Lastly, the height of the sole can be minimized by simply translating the rocker sole shape proximally, see FIG. 5B. The shoe sole can be directly cut to the rocker form, FIG. 6A, and can also be finished into a flat soled rocker shoe for cosmetic reasons (see FIG. 6B). In FIG. 6B, the non-rocker portion NRP of the shoe sole is made of a highly compressible material wherein the void 50 left after cutting of the roll-over profile shape in the shoe sole is filled by joining a highly compressible foam filler material to the roll-over profile shape to disguise its appearance.

The present invention has many potential commercial applications including, but not limited to, a) fotwear for the general public—certain rocker shapes may promote better balance in able-bodied persons or simply feel more comfortable during walking. Shoes that minimize ankle movement during single limb support would largely utilize isometric contractions of muscles crossing the ankle joint and b) orthopedic rocker shoes—they may be beneficial to patients with foot and ankle problems to reduce their movement of ankle-foot joints during the highest loading period of walking. It is possible that ankle pain and ankle joint wear are linked to movements of the ankle while under high loads. This idea is logical mechanically because friction is directly related to the amount of normal force between two objects. Reducing ankle motion naturally with muscles surrounding the leg would limit the amount of atrophy in these muscles and may still allow plantarflexion of the ankle in late stance phase to improve walking balance. Also, these shoes could be made in a variety of styles (see other shoe lines including the Masai Barefoot Technology (MBT) and the Gravity Defying shoes (featured often in the SkyMall magazine).

Although the invention has been described with respect to certain embodiments thereof, those skilled in the art will appreciate that changes and modifications can be made therein within the scope of the invention as defined in the appended claims.

References, Which are Incorporated Herein by Reference:

Adamczyk, P. G., Collins, S. H. and Kuo, A. D. (2006). The advantages of a rolling foot in human walking. J Exp Biol 209, 3953-3963,

Brown, D., Wertsch, J. J., Harris, G. F., Klein, J. and Janisse, D. (2004). Effect of rocker soles on plantar pressures. Arch Phys Med Rehabil 85(1), 81-6.

Collins, S., Ruina, A., Tedrake, R., Wisse, M. (2005). Efficient bipedal robots based on passive-dynamic walkers. Science 307, 1082-1085.

Crenshaw, S. J., Polio, F. E. and Brodsky, J. W. (2004). The effect of ankle position on plantar pressure in a short leg walking boot. Foot Ankle Int 25(2), 69-72.

de Lateur, B. J., Giaconi, R. M., Questad, K., Ko, M. and Lehmann, J. F. (1991). Footwear and posture. Compensatory strategies for heel height. Am J Phys Med Rehabil 70(5), 246-54.

Hansen, A. H. (2002). Roll-over characteristics of human walking with applications for artificial limbs. Ph.D. thesis, Evanston, Northwestern University.

Hansen, A. H., Meier, M. R., Sam, M., Childress, D. S. and Edwards, M. L. (2003). Alignment of trans-tibial prostheses based on roll-over shape principles. Prosthet Orthot Int 27(2), 89-99.

Hansen, A. H., Childress, D. S. and Knox, E. H. (2004a). Roll-over shapes of human locomotor systems: effects of walking speed. Clin Biomech 19(4), 407-14.

Hansen, A. H., Childress, D. S. and Miff, S. C.. (2004b). Roll-over charateristics of human walking on inclined surfaces, Hum Movement Sci. 23(6), 807-821.

Hansen, A. H. and Childress, D. S. (2004). Effects of shoe heel height on biologic roll-over characteristics during walking. J Rehabil Res Dev 41(4), 547-554.

Hansen, A. H. and Childress, D. S. (2005) Effects of Adding Weight to the Torso on Roll-over Characteristics of Walking. J Rehabil Res Dev, 42(3), 381-390.

Hullin, M. G. and Robb, J. E. (1991). Biomechanical effects of rockers on walking in a plaster cast. J Bone Joint Surg Br 73(1), 92-5.

Knox, E. H. (1996). The role of prosthetic feet in walking. Ph.D. thesis, Evanston, Northwestern University.

McGeer, T. (1990). Passive dynamic walking. Int J Robot Res 9(2), 62-82.

Milgram, J. E. and Jacobson, M. A. (1978). Footgear: therapeutic modifications of sole and heel. Orthopaedic Review 7(11), 57-62.

Morawski, J. and Wojcieszak, l. (1978). Miniwalker—a resonant model of human locomotion. Biomechanics VIA. E. Asmussen, Jorgensen, K. Baltimore, University Park Press. 2A: 445-451.

Mueller, M. J. and Diamond, J. E. (1988). Biomechanical treatment approach to diabetic plantar ulcers. A case report. Phys Ther 68(12), 1917-20.

Mueller, M. J., Strube, M. J. and Allen, B. T. (1997). Therapeutic footwear can reduce plantar pressures in patients with diabetes and transmetatarsal amputation. Diabetes Care 20(4), 637-41.

Mueller, M. J. and Strube, M. J. (1997). Therapeutic footwear: enhanced function in people with diabetes and transmetatarsal amputation. Arch Phys Med Rehabil 78(9), 952-6.

Nawoczenski, D. A., Birke, J. A. and Coleman, W. C. (1988). Effect of rocker sole design on plantar forefoot pressures. J Am Podiatr Med Assoc 78(9), 455-60.

Opila, K. A., Wagner, S. S., Schiowitz, S. and Chen, J. (1988). Postural alignment in barefoot and high-heeled stance. Spine 13(5), 542-7.

Perry, J., Gronley, J. K. and Lunsford, T. (1981). Rocker shoe as walking aid in multiple sclerosis. Arch Phys Med Rehabil 62(2), 59-65.

Perry, J. (1992). Gait Analysis: Normal and Pathological Function. Thorofare, SLACK Incorporated.

Peterson, M. J., Perry, J. and Montgomery, J. (1985). Walking patterns of healthy subjects wearing rocker shoes. Phys Ther 65(10), 1483-9.

Postema, K., Burm, P. E., Zande, M. E. and Limbeek, J. (1998). Primary metatarsalgia: the influence of a custom moulded insole and a rockerbar on plantar pressure. Prosthet Orthot Int 22(1), 35-44.

Praet, S. F. and Louwerens, J. W. (2003). The influence of shoe design on plantar pressures in neuropathic feet. Diabetes Care 26(2), 441-5.

Richardson, J. K. (1991). Rocker-soled shoes and walking distance in patients with calf claudication. Arch Phys Med Rehabil 72(8), 554-8.

Rosenfield, J. S. and Trepman, E. (2000). Treatment of sesamoid disorders with a rocker sole shoe modification. Foot Ankle Int 21(11), 914-5.

Ryschon, T. W., Fowler, M. D., Wysong, R. E., Anthony, A. -R. and Balaban, R. S. (1997). Efficiency of human skeletal muscle in vivo: comparison of isometric, concentric, and eccentric muscle contraction. J Appi Physiol 83(3), 867-874.

Sam, M., Childress, D. S., Hansen, A. H., Meier, M. R., Lambla, S., Grahn, E. C., Rofock, J. S. (2004). The Shape&Roll prosthetic foot (Part 1): Design and development of appropriate technology for low-income countries. Med Confl Surviv 20(4), 294-306.

Schaff, P. S. and Cavanagh, P. R. (1990). Shoes for the insensitive foot: the effect of a “rocker bottom” shoe modification on plantar pressure distribution. Foot Ankle 11(3), 129-40.

Trepman, E. and Yeo, S. J. (1995). Nonoperative treatment of metatarsophalangeal joint synovitis. Foot Ankle Int 16(12), 771-7.

Van Schie, C., Ulbrecht, J. S., Becker, M. B. and Cavanagh, P. R. (2000). Design criteria for rigid rocker shoes. Foot Ankle Int 21(10), 833-44.

Wisse, M. and van Frankenhuyzen, J. (2003). Design and Construction of MIKE; a 2D autonomous biped based on passive dynamic walking. Proceedings of the AMAM Conference Of Adaptive Motion of Animals and Machines, Kyoto, Japan. 

1. A method of providing a shoe sole profile shape for an individual, comprising determining a shoe sole geometry that provides a roll-over shape for level ground walking that accommodates a prescribed ankle angular motion of the individual and imparting the shoe sole geometry to a shoe sole.
 2. The method of claim 1 including determining respective radial distances between a reference shoe sole surface when the ankle is rotated to respective angles during at least partial heel-to-toe motion and an invariant roll-over shape arc.
 3. The method of claim 2 including shaping the shoe sole profile using said radial distances.
 4. The method of claim 3 including machining or molding the shoe sole profile.
 5. A shoe having a sole profile determined by the method of claim
 1. 